Sir Alex Ferguson's delight at Manchester United's 2-1 win over Liverpool was tempered by injury concerns about his captain, Nemanja Vidic, and Ashley Young, who left the ground on crutches. For Wednesday's FA Cup third-round replay visit of West Ham, the United manager could also be without Jonny Evans, who suffered a hamstring problem on Saturday.

Although United were unable to confirm the nature of the injuries sustained against Liverpool, each is thought to be a knee problem. Vidic is only four games into a return from a second serious knee injury suffered during the past 13 months and he admitted recently that United's medical department is carefully choosing which games he plays during the first months of his comeback. The captain appeared to have a problem after an aerial challenge on 65 minutes in which he also clashed heads but played on until he was replaced by Chris Smalling 10 minutes from the end. Young was substituted at half-time following his heavy tackle on Daniel Agger just past the half-hour that caused his injury.

Vidic's goal 10 minutes after the interval turned out to be the winner, doubling the lead Robin van Persie gave United in the first half. Daniel Sturridge's second goal for Liverpool came moments after Vidic had deflected a Patrice Evra header into the net.

"I would have taken that score before the game," Ferguson said. "The first-half performance, and until we scored the second goal, was absolutely magnificent, it was as good as a performance we've had for a long time. But when they got the goal they were inspired – their supporters got going and it was hard work after that to be honest and I'm just glad we won."

Sturridge's goal came two minutes after United's second, with the striker beating Rafael da Silva to the rebound after David de Gea palmed away Steven Gerrard's shot. Ferguson was unhappy that the right-back had not reacted quicker.

"I haven't seen the goal again," he said. "I haven't looked at it – to me it was a bit soft for us. Once again the goalie's parried one out and nobody's following in the rebounds and it lifted them, that's without doubt. But some of our defending after that was a bit erratic, desperate even at times but we managed to get through it.

"The name of the game is when you're playing the big games there are moments when you have to defend and today [there were some] of them. Winning these games is important, it doesn't matter what position we are in the league." Regarding Evans, the manager added: "He felt his hamstring [on Saturday] afternoon."

Brendan Rodgers, the Liverpool manager, was heartened by his side's second-half performance. "We're 24 points behind United now," he said. "But we're not 24 points behind in terms of quality. The points difference is due to the squad. Once we close the gap in the squad in the coming transfer windows, I've got great faith that we'll be able to challenge."